Question 12 Marks
Subtract:
$6 x^3-7 x^2+5 x-3$ from $4-5 x+6 x^2-8 x^3$
Answer$6 x^3-7 x^2+5 x-3$ from $4-5 x+6 x^2-8 x^3$
$=4-5 x+6 x^2-8 x^3-\left(6 x^3-7 x^2+5 x-3\right)$
$=4-5 x+6 x^2-8 x^3-6 x^3+7 x^2-5 x+3$
$=7-10 x+13 x^2-14 x^3$
$=-14 x^3+13 x^2-10 x+7$
View full question & answer→Question 22 Marks
Subtract: -
$-11 x^2 y^2+7 x y-6$ from $9 x^2 y^2-6 x y+9$
Answer$\quad-11 x^2 y^2+7 x y-6$ from $9 x^2 y^2-6 x y+9$
$=9 x^2 y^2-6 x y+9-\left(-11 x^2 y^2+7 x y-6\right)$
$=9 x^2 y^2-6 x y+9+11 x^2 y^2-7 x y+6$
$=20 x^2 y^2-13 x y+15$
$=15-13 x y+20 x^2 y^2$
$=20 x^2 y^2-13 x y+15$
View full question & answer→Question 32 Marks
If p = -2, q = -1 and r = 3, find the value of:
p - q - r
AnswerSubstituting p = -2, q = -1 and r = 3 in the given expression, we get:
p - q - r = (-2) - (-1) - 3
= -2 + 1 - 3 = -4
View full question & answer→Question 42 Marks
Add:
$x^3+y^3-z^3+3 x y z-x^3+y^3+z^3-6 x y z, x^3-y^3-z^3-8 x y z$
Answer$x^3+y^3-z^3+3 x y z,-x^3+y^3+z^3-6 x y z, x^3-y^3-z^3-8 x y z$
$=x^3+y^3-z^3+3 x y z+\left(-x^3\right)+y^3+z^3-6 x y z+x^3-y^3-z^3-8 x y z$
$=\left(x^3-x^3+x^3\right)+\left(y^3+y^3-y^3\right)-\left(z^3-z^3+z^3\right)+(3 x y z-6 x y z-8 x y z)$
$=x^3+y^3-z^3-11 x y z$
View full question & answer→Question 52 Marks
Simplify:
$2 p^3-3 p^2+4 p-5-6 p^3+2 p^2-8 p-2+6 p+8$
Answer$2 p^3-3 p^2+4 p-5-6 p^3+2 p^2-8 p-2+6 p+8$
$=2 p^3-6 p^3-3 p^2+2 p^2+4 p+6 p-5-2+8$
$=-6 p^3-p^2+10 p+1$
View full question & answer→Question 62 Marks
If $p =-2, q =-1$ and $r =3$, find the value of:
$3 p^2 q+5 p q^2+2 p q r$
AnswerSubstituting $p=-2, q=-1$ and $r=3$ in the given expression, we get:
$3 p^2 q+5 p q^2+2 p q r$
$=3 \times(-2)^2 \times(-1)+5 \times(-2) \times(-1)^2+2 \times(-2) \times(-1) \times 3$
$=3 \times 4 \times(-1)+5 \times(-2) \times 1+12$
$=-12-10+12=-10$
View full question & answer→Question 72 Marks
Subtract:
$a^2-b^2$ from $b^2-a^2$
Answer$=b^2-a^2-\left(a^2-b^2\right)$
$=b^2-a^2-a^2+b^2$
$=2 b^2-2 a^2$
View full question & answer→Question 82 Marks
Add:
$2+x-x^2+6 x^3,-6-2 x+4 x^2-3 x^3, 2+x^2, 3-x^3+4 x-2 x^2$
Answer$2+x-x^2+6 x^3,-6-2 x+4 x^2-3 x^3, 2+x^2, 3-x^3+4 x-2 x^2$
$=2+x-x^2+6 x^3+(-6)-2 x+4 x^2-3 x^3+2+x^2+3-x^3+4 x-2 x^2$
$=(2-6+2+3)+(x-2 x+4 x)-\left(x^2-4 x^2-x^2+2 x^2\right)+\left(6 x^3-3 x^3-x^3\right)$
$=1+3 x+2 x^2+2 x^3$
View full question & answer→Question 92 Marks
If $p=-2, q=-1$ and $r=3$, find the value of:
$p^2+q^2-r^2$
AnswerSubstituting $p=-2, q=-1$ and $r=3$ in the given expression, we get:
$p^2+q^2-r^2=(-2)^2+(-1)^2-(3)^2$
$=4+1-9$
$=5-9=-4$
View full question & answer→Question 102 Marks
Add:
$x^2-a^2,-5 x^2+2 a^2,-4 x^2+4 a^2$
Answer$x^2-a^2,-5 x^2+2 a^2,-4 x^2+4 a^2$
$=x^2-a^2+\left(-5 x^2\right)+2 a^2+\left(-4 x^2\right)+4 a^2$
$=x^2-a^2-5 x^2+2 a^2-4 x^2+4 a^2$
$=\left(x^2-5 x^2-4 x^2\right)-\left(a^2-2 a^2-4 a^2\right)$
$=x^2-9 x^2-\left(a^2-6 a^2\right)$
$=8 x^2-\left(-5 a^2\right)$
$=-8 x^2+5 a^2=5 a^2-8 x^2$
View full question & answer→Question 112 Marks
If $p=-2, q=-1$ and $r=3$, find the value of:
$p^3+q^3+r^3+3 p q r$
AnswerSubstituting $p=-2, q=-1$ and $r=3$ in the given expression, we get:
$p^3+q^3+r^3+3 p q r$
$=(-2)^3+(-1)^3+(3)^3+3 \times(-2) \times(-1) \times 3$
$=(-8)+(-1)+27+18$
$=-8-1+27+18$
$=-9+45=36$
View full question & answer→Question 122 Marks
Simplify:
4x - (3y - x + 2z)
AnswerWe have:
4x - (3y - x + 2z)
= 4x - 3y + x - 2z
= 4x + x - 2y - 2z
= 5x - 3y - 2z
View full question & answer→Question 132 Marks
Add:
7xyz, -5xyz, 9xyz, -8xyz
Answer= 7xyz + (-5xyz) + 9xyz + (-8xyz)= 7xyz - 5xyz + 9xyz - 8xyz
= (7xyz + 9xyz) - (5xyz + 8xyz)
= 16xyz - 13xyz = 3xyz
View full question & answer→Question 142 Marks
Add:
$6 a^3,-4 a^3, 10 a^3,-8 a^3$
Answer$=6 a^3+\left(-4 a^3\right)+10 a^3+\left(-8 a^3\right)$
$=\left(6 a^3+10 a^3\right)-\left(4 a^3+8 a^3\right)$
$=16 a^3-12 a^3=4 a^3$
View full question & answer→Question 152 Marks
Add:
3a - 2b + 5c, 2a + 5b - 7c, - a - b + c
Answer3a - 2b + 5c, 2a + 5b - 7c, - a - b + c
= 3a - 2b + 5c, 2a + 5b - 7c, -a - b + c
= (3a + 2a - a) - (2b - 5b + b) + (5c - 7c + c)
= 4a - (3b - 5b) + (6c - 7c)
= 4a + 2b - c
View full question & answer→Question 162 Marks
Add:
$2 x^3-3 x^2+7 x-8,-5 x^3+2 x^2-4 x+1,3-6 x+5 x^2-x^3$
Answer$2 x^3-3 x^2+7 x-8,-5 x^3+2 x^2-4 x+1,3-6 x+5 x^2-x^3$
$=2 x^3-3 x^2+7 x-8+\left(-5 x^3\right)+2 x^2-4 x+1+3-6 x+5 x^2-x^3$
$=\left(2 x^3-5 x^3-x^3\right)-\left(3 x^2-2 x^2-5 x^2\right)+(7 x-4 x-6 x)-(8-1-3)$
$=\left(2 x^3-6 x^3\right)-\left(3 x^2-7 x^2\right)+(7 x-10 x)-(8-4)$
$=-4 x^3+4 x^2-3 x-4$
View full question & answer→Question 172 Marks
Write the following using literals, numbers and signs of basic operations:
One-third of x multiplied by the sum of a and b.
AnswerOne-third of x is $\frac{\text{x}}{3}.$
The sum of a and b is (a + b)
$\therefore$ One third of x multiplied by the sum of a and b
$=\frac{\text{x}}{3}\times(\text{a + b})=\frac{\text{x}(\text{a + b})}{3}$
View full question & answer→Question 182 Marks
Add:
$2 x^2,-3 x^2, 7 x^2$
Answer$=2 x^2+\left(-3 x^2\right)+7 x^2$
$=9 x^2-3 x^2=6 x^2$
View full question & answer→Question 192 Marks
How much less than x - 2y + 3z is 2x - 4y - z?
Answer= (x - 2y + 3z) - (2x - 4y - z)= x - 2y + 3z - 2x + 4y + z
= -x + 2y + 4z
View full question & answer→Question 202 Marks
Subtract:
-2a + b + 6d from 5a - 2b - 3c
Answer-2a + b + 6d from 5a - 2b - 3c
= 5a - 2b - 3c - (-2a + b + 6d)
= 5a - 2b - 3c + 2a - b - 6d
= 7a - 3b - 3c - 6d
View full question & answer→Question 212 Marks
If$ x = 1, y = 2$ and $z = 5$, find the value of:$2x^2 - 3y^2 + z^2$
AnswerSubstituting $x = 1, y = 2$ and $z = 5$ in the given expression, we get:
$2x^2 - 3y^2 + z^2 = 2 \times (1)^2 - 3 \times (2)^2 + (5)^2$
$= 2 \times 1 - 3 \times 4 + 25$
$= 2 - 12 + 25$
$= 27 - 12 = 15$
View full question & answer→Question 222 Marks
If x = 1, y = 2 and z = 5, find the value of:3x – 2y + 4z
AnswerSubstituting x = 1, y = 2 and z = 5 in the given expression, we get:
3x - 2y + 4z = 3 × 1 - 2 × 2 + 4 × 5
= 3 - 4 + 20 = 23 - 4 = 19
View full question & answer→Question 232 Marks
If $x=1, y=2$ and $z=5$, find the value of:
$x^2+y^2+z^2$
AnswerSubstituting $x=1, y=2$ and $z=5$ in the given expression, we get:
$x^2+y^2+z^2=(1)^2+(2)^2+(5)^2$
$=1+4+25=30$
View full question & answer→Question 242 Marks
By how much does 1 exceed 2x - 3y - 4?
Answer= 1 - (2x - 3y - 4)= 1 - 2x + 3y + 4
= 5 - 2x + 3y
View full question & answer→Question 252 Marks
By how much does $3 x^2-5 x+6$ exceed $x^3-x^2+4 x-1$ ?
Answer$=\left(3 x^2-5 x+6\right)-\left(x^3-x^2+4 x-1\right)$
$=3 x^2-5 x+6-x^3+x^2-4 x+1$
$=-x^3+4 x^2-9 x+7$
View full question & answer→Question 262 Marks
What must be subtracted from $a^3-4 a^2+5 a-6$ to obtain $a^2-2 a+1$ ?
Answer$=a^3-4 a^2+5 a-6-\left(a^2-2 a+1\right)$
$=a^3-4 a^2+5 a-6-a^2+2 a-1$
$=a^3-5 a^2+7 a-7$
View full question & answer→Question 272 Marks
Simplify:
$x^4-6 x^3+2 x-7+7 x^3-x+5 x^2+2-x^4$
Answer$x^4-6 x^3+2 x-7+7 x^3-x+5 x^2+2-x^4$
$=x^4-x^4-6 x^3+7 x^3+5 x^2+2 x-x-7+2$
$=x^3+5 x^2+x-5$
View full question & answer→Question 282 Marks
Simplify:
$2 x^2-x y+6 x-4 y+5 x y-4 x+6 x^2+3 y$
Answer$2 x^2-x y+6 x-4 y+5 x y-4 x+6 x^2+3 y$
$=2 x^2+6 x^2-x y+5 x y+6 x-4 x-4 y+3 y$
$=8 x^2+4 x y+2 x-y$
View full question & answer→Question 292 Marks
Write the following using literals, numbers and signs of basic operations:
The product of x and y added to their sum.
AnswerThe product of x and y is xy
The sum of x and y is (x + y)
So, product of x and y added to their sum is xy + (x + y)
View full question & answer→Question 302 Marks
Subtract:
$x^3+2 x^2 y+6 x y^2-y^3$ from $y^3-3 x y^2-4 x^2 y$
Answer$x^3+2 x^2 y+6 x y^2-y^3$ from $y^3-3 x y^2-4 x^2 y$
$=y^3-3 x y^2-4 x^2 y-\left(x^3+2 x^2 y+6 x y^2-y^3\right)$
$=y^3-3 x y^2-4 x^2 y-x^3-2 x^2 y-6 x y^2+y^3$
$=2 y^3-9 x y^2-6 x^2 y-x^3$
$=-x^3+2 y^3-6 x^2 y-9 x y^2$
View full question & answer→Question 312 Marks
Subtract:
5a + 7b - 2c from 3a - 7b + 4c
Answer5a + 7b - 2c from 3a - 7b + 4c
= (3a - 7b + 4c) - (5a + 7b - 2c)
= 3a - 7b + 4c - 5a - 7b + 2c
= -2a - 14b + 6c
View full question & answer→Question 322 Marks
If $x=1, y=2$ and $z=5$, find the value of:
$2 x^2 y-5 y z+x y^2$
AnswerSubstituting $x=1, y=2$ and $z=5$ in the given expression, we get:
$2 x^2 y-5 y z+x y^2$
$=2 \times(1)^2 \times 2-5 \times 2 \times 5+1 \times(2)^2$
$=2 \times 1 \times 2-10 \times 5+1 \times 4$
$=4-50+4$
$=8-50=-42$
View full question & answer→Question 332 Marks
AnswerWe have:
a - (b - 2a)
= a - b + 2a
= a + 2a - b
= (1 + 2) a - b
= 3a - b
View full question & answer→Question 342 Marks
By how much is 2x - 3y + 4z greater than 2x + 5y - 6z + 2?
Answer= (2x - 3y + 4z) - (2x + 5y - 6z + 2)= 2x - 3y + 4z - 2x - 5y + 6z - 2
= -8y + 10z - 2
View full question & answer→Question 352 Marks
If x = 1, y = 2 and z = 5, find the value of:xy + yz - zx
AnswerSubstituting x = 1, y = 2 and z = 5 in the given expression, we get:
xy + yz - zx = 1 × 2 + 2 × 5 - 5 × 1
= 2 + 10 - 5
= 12 - 5 = 7
View full question & answer→Question 362 Marks
How much is a + 2a - 3c greater than 2a - 3b + c?
Answer= (a + 2a - 3c) - (2a - 3b + c)= a + 2a - 3c - 2a + 3b - c
= -a + 5b - 4
View full question & answer→Question 372 Marks
Subtract:
a - 2b - 3c from -2a + 5b - 4c
Answera - 2b - 3c from -2a + 5b - 4c
= -2a + 5b - 4c - (a - 2b - 3c)
= -2a + 5b - 4c - 4 + 2b + 3c
= -3a + 7b - c
View full question & answer→Question 382 Marks
Subtract:
$5 x^2-3 x y+y^2$ from $7 x^2-2 x y-4 y^2$
Answer$5 x^2-3 x y+y^2$ from $7 x^2-2 x y-4 y^2$
$=7 x^2-2 x y-4 y^2-\left(5 x^2-3 x y+y^2\right)$
$=7 x^2-2 x y-4 y^2-5 x^2+3 x y-y^2$
$=2 x^2+x y-5 y^2$
$=2 x^2-5 y^2+x y$
View full question & answer→Question 392 Marks
If $p =-2, q =-1$ and $r =3$, find the value of:
$p^4+q^4-r^4$
AnswerSubstituting $p =-2, q =-1$ and $r =3$ in the given expression, we get:
$p^4+q^4-r^4=(-2)^4+(-1)^4-(3)^4$
$=16+1-81$
$=17-81=-64$
View full question & answer→Question 402 Marks
Add:
8a - 6ab + 5b, -6a - ab - 8b, -4a + 2ab + 3b
Answer8a - 6ab + 5b, -6a - ab - 8b, -4a + 2ab + 3b
= 8a - 6ab + 5b + (-6a) - ab - 8b + (-4a) + 2ab + 3b
= (8a - 6a - 4a) - (6ab + ab - 2ab) + (5b - 8b + 3ab)
= -2a - (7ab - 2ab) + (8b - 8b)
= -2a - 5ab
View full question & answer→Question 412 Marks
Add:
$2 x^2-8 x y+7 y^2-8 x y^2, 2 x y^2+6 x y-y^2+3 x^2, 4 y^2-x y-x^2+x y^2$
Answer$2 x^2-8 x y+7 y^2-8 x y^2, 2 x y^2+6 x y-y^2+3 x^2, 4 y^2-x y-x^2+x y^2$
$=2 x^2-8 x y+7 y^2-8 x y^2+2 x y^2+6 x y-y^2+3 x^2+4 y^2-x y-x^2+x y^2$
$=\left(2 x^2+3 x^2-x^2\right)-(8 x y-6 x y+x y)+\left(7 y^2-y^2+4 y^2\right)-\left(8 x y^2-2 x y^2-x y^2\right)$
$=\left(5 x^2-x^2\right)-(9 x y-6 x y)+\left(11 y^2-y^2\right)-\left(8 x y^2-3 x y^2\right)$
$=4 x^2-3 x y+10 y^2-5 x y^2$
View full question & answer→Question 422 Marks
If $x=1, y=2$ and $z=5$, find the value of:
$x^3-y^3-z^3$
AnswerSubstituting $x=1, y=2$ and $z=5$ in the given expression, we get:
$x^3-y^3-z^3=(1)^3-(2)^3-(5)^3$
$=(1 \times 1 \times 1)-(2 \times 2 \times 2)-(5 \times 5 \times 5)$
$=1-8-125$
$=1-133=-132$
View full question & answer→Question 432 Marks
If $p=-2, q=-1$ and $r=3$, find the value of:
$2 p^2-q^2+3 r^2$
AnswerSubstituting $p =-2, q =-1$ and $r =3$ in the given expression, we get:
$2 p^2-q^2+3 r^2$
$=2 \times(-2)^2-(-1)^2+3 \times(3)^2$
$=2 \times 4-1+3 \times 9$
$=8-1+27=34$
View full question & answer→